double.truncation (version 1.7)

PMLE.SEF2.negative: Parametric Inference for the two-parameter SEF model (negative parameter space for eta_2)

Description

Maximum likelihood estimates and their standard errors (SEs) are computed. Also computed are the likelihood value, AIC, and other qnantities. Since this is the model, estimates for the mean and SD are also computed.

Usage

PMLE.SEF2.negative(u.trunc, y.trunc, v.trunc, epsilon = 1e-04)

Value

eta

estimates

SE

standard errors

convergence

Log-likelihood, degree of freedom, AIC, the number of iterations

Score

score vector at the converged value

Hessian

Hessian matrix at the converged value

Arguments

u.trunc

lower truncation limit

y.trunc

variable of interest

v.trunc

upper truncation limit

epsilon

error tolerance for Newton-Raphson

Author

Takeshi Emura, Ya-Hsuan Hu

Details

Details are seen from the references.

References

Hu YH, Emura T (2015) Maximum likelihood estimation for a special exponential family under random double-truncation, Computation Stat 30 (4): 1199-229

Emura T, Hu YH, Konno Y (2017) Asymptotic inference for maximum likelihood estimators under the special exponential family with double-truncation, Stat Pap 58 (3): 877-909

Dorre A, Emura T (2019) Analysis of Doubly Truncated Data, An Introduction, JSS Research Series in Statistics, Springer

Examples

### Data generation: see Appendix of Hu and Emura (2015)
n=300
eta1_true=30
eta2_true=-0.5
mu_true=30
mu_u=29.09
mu_v=30.91

a=u=v=y=c()

###generate n samples of (ui,yi,vi) subject to ui<=yi<=vi###
j=1
repeat{  
  u[j]=rnorm(1,mu_u,1)
  v[j]=rnorm(1,mu_v,1)
  y[j]=rnorm(1,mu_true,1)
  if(u[j]<=y[j]&&y[j]<=v[j]) a[j]=1 else a[j]=0
  if(sum(a)==n) break ###we need n data set###
  j=j+1
}
mean(a) ### inclusion probability around 0.5 ###

v.trunc=v[a==1]
y.trunc=y[a==1]
u.trunc=u[a==1]
  
PMLE.SEF2.negative(u.trunc,y.trunc,v.trunc)